Ah - OK. Thanks. I wll check out "WordpressInstanceProperties" field "cache".
The ISSUE was that no matter what someone did within a WP site's Administrator Interface, WP Toolkit was not showing any value in the "Name" field. Yet, after the Plesk daily maintenance, the WP Toolkit now, "magically", has a value to display in the "Name" field.
SO - the question was: WHERE did WP Toolkit GET "that value" so I could reasonably be able to diagnose WHY "that value" was not appearing, and later "where" it came from so that I could find it, view it, and verify it.
There is a four-way association with the WP Toolkit "Name" field":
1) WP site Settings/Site Title field (site WP DB "blogname" column)
2) Plesk PSA DB "WordpressInstanceProperties" field name is "cache"
3) Plesk daily maintenance which copies the value from #1 to #2
4) #3 only happens once per day